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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Functions

NDA 2015 · Mathematics · Functions

f(x y)=f(x)+f(y) is true for all

f(xy)=f(x)+f(y)f(x y)=f(x)+f(y) is true for all

Options

  1. APolynomial functions f
  2. BTrigonometric functions f
  3. CExponential functions f
  4. DLogarithmic functions f

Correct answer

D. Logarithmic functions f

Step-by-step solution

 Let f(x)=log⁡x∴f(y)=log⁡yf(xy)=log⁡(xy)=log⁡x+log⁡y⇒f(xy)=f(x)+f(y)\begin{aligned} & \text{ Let } \mathrm{f}(\mathrm{x})=\log \mathrm{x} \\ & \therefore \mathrm{f}(\mathrm{y})=\log \mathrm{y} \\ & & \mathrm{f}(\mathrm{xy})=\log (\mathrm{xy})=\log \mathrm{x}+\log \mathrm{y} \\ & \Rightarrow \mathrm{f}(\mathrm{xy})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})\end{aligned}
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